A ring (2 kg, r = 2 m) rotates in a CW direction with initial angular velocity 2

Question

A ring (2 kg, r = 2 m) rotates in a CW direction with initial angular velocity 20 s-1. A disk (8 kg, r = 2 m) rotates in a CCW direction with initial angular velocity 60 s-1. The ring and disk "collide" and eventually rotate together. Assume that positive angular momentum and angular velocity values correspond to rotation in the CCW direction.

What is the initial angular momentum Li of the ring+disk system? kg m2 s Submit Answer Tries 0/3 What is the final angular velocity Of of the ring+disk system? -1 Submit Answer Tries 0/3

Explanation / Answer

Mass of ring is m = 2kg

radius of ring is r = 2m

Initial angular velocity of ring is r = -20rad/s (negative because it's is CW direction and CCW is positive direction)

Mass of ring is M = 8kg

radius of ring is R = 2m

Initial angular velocity of ring is d = 60rad/s

Moment of Inertia of ring is Ir = mr2 = (2kg)(2m)2 = 8kg-m2

Moment of Inertia of disc is Id = MR2/2 = (8kg)(2m)2/2 = 16kg-m2

So, initial angular momentum of the ring + disc system is:

Li  = Irr + Idd

or Li  = (8kg-m2)(-20rad/s) + (16kg-m2)(60rad/s)

or Li = -160kg-m2/s + 960kg-m2

or Li = 800kg-m2/s

Thus, initial angular momentum of the ring + disc system is Li = 800kg-m2/s

Let the final angular velocity of the ring+disc system be .

Let the final angular momentum be Lf

Using conservation of meomentum we have:

Li =  Lf

or  800kg-m2/s = (Ir + Id) =  (8kg-m2 + 16kg-m2) = (24kg-m2)

or = 33.33rad/s

So, final angular velocity of the ring+disc system will be =  33.33rad/s

This concludes the answers. Check the answer and let me know if it's correct. If you need anymore clarification or correction I will be happy to oblige....

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